Umeå University, Mathematics and Mathematical Statistics

Position ID: 2216-PHD3 [#20353]
Position Title: PhD student in mathematical statistics within the WASP AI programme
Position Type: Other
Position Location: Umea, Vasterbottens Lan 901 87, Sweden [map]
Subject Areas: Mathematical statistics, focusing on geometric deep learning
Application Deadline: 2022/09/19 11:59PMhelp popup (posted 2022/08/08, listed until 2022/09/19)
Position Description:    

*** the listing date or deadline for this position has passed. ***

The Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematical statistics, focusing on geometric deep learning. The position is for four years of doctoral studies, including participation in research and postgraduate courses. The last day to apply is September 19, 2022.

Project description and tasks:

Machine learning, especially deep neural networks, has, during the early 21st century, had an immense impact on both research and society at large. This rapid development has made great progress possible and caused significant challenges. A subfield within machine learning is so-called geometric deep learning. This concept can mean many things, but at its core, the field is dealing with situations in which the in-data is of non-standard type. One can, for instance, consider 3D models, point clouds, or spherical images. To deal with such data poses special requirements on the network architectures.

One of the more interesting questions is the one of so-called equivariance. An essential property of the popular convolutional neural networks is translation equivariance; a translation of the in-data causes a translation of the out-data. With in-data of different types comes the need for equivariance with respect to other groups of transformations, both of discrete and continuous type. Examples of exciting research questions are how such networks can be constructed, how they can be trained, and their mathematical properties.

This project aims to develop new methods and new theories within geometric deep learning. This can, for instance, consist of the design of new network architectures, analysis of universality properties, explorations of a new class of transformations, and applications to simulated and real data. The PhD candidate is also expected to cooperate with our other ongoing AI-related projects.

The project is a part of the AI/Math track within Wallenberg AI, Autonomous Systems and Software Program (WASP), and the PhD student will take part in the WASP graduate school, see for more information.


To be admitted for studies at the third-cycle level, the applicant is required to have completed a second-cycle level degree, or completed course requirements of at least 240 ECTS credits, of which at least 60 ECTS credits are at second-cycle level, or have an equivalent education from abroad, or equivalent qualifications. For third-cycle studies in mathematical statistics, the applicant must have completed at least 60 credits within the field of mathematical statistics, statistics and mathematics, of which at least 15 credits shall have been acquired at the second-cycle level.

Excellent skills in programming (preferably MatLab or Python) are required. Good knowledge in both written and spoken English is also a requirement. Documented knowledge and experience in signal processing, machine learning, image analysis, differential geometry, and representation theory are merits.

You are expected to take on an active role within this project and institutional work. You have a scientific mindset, can work independently, and are structured, flexible and solution-oriented. Above all, you are determined to continuously develop your skills and contribute to mathematical machine learning research.

Applications will be assessed by the applicant’s qualification and ability to benefit from the graduate education they will receive.

More information about the Department of Mathematics and Mathematical Statistics:

Umeå offers excellent working and living conditions. The city is young and located right next to a large river. It is surrounded by forests and lakes and lies close by the sea. In the vicinity there are plenty of opportunities for both indoor and outdoor activities.

For further information and instructions on how to apply, see:

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Contact: Jun Yu
Postal Mail:
Department of Mathematics and Mathematical Statistics
Umeå University
901 87 Umeå
Web Page: